An energy-based finite-strain model for 3D heterostructured materials and its validation by curvature analysis

Abstract

This paper presents a comprehensive study of the intrinsic strain response of 3D heterostructures arising from lattice mismatch. Combining materials with different lattice constants induces strain, leading to the bending of these heterostructures. We propose a model for nonlinear elastic heterostructures such as bimetallic beams or nanowires that takes into account local prestrain within each distinct material region. The resulting system of partial differential equations (PDEs) in Lagrangian coordinates incorporates a nonlinear strain and a linear stress-strain relationship governed by Hooke's law. To validate our model, we apply it to bimetallic beams and hexagonal hetero-nanowires and perform numerical simulations using finite element methods (FEM). Our simulations examine how these structures undergo bending under varying material compositions and cross-sectional geometries. In order to assess the fidelity of the model and the accuracy of simulations, we compare the calculated curvature with analytically derived formulations. We derive these analytical expressions through an energy-based approach as well as a kinetic framework, adeptly accounting for the lattice constant mismatch present at each compound material of the heterostructures. The outcomes of our study yield valuable insights into the behavior of strained bent heterostructures. This is particularly significant as the strain has the potential to influence the electronic band structure, piezoelectricity, and the dynamics of charge carriers.